This work unveils a novel and fundamental connection between structured light and topological field theory by showing how the natural geometrical setting for paraxial vector beams is that of an $\text{SU}\left(2\right)$ principal bundle over ${\mathbb{R}}^{2+1}$. Going beyond the usual high-order Poincaré sphere approach, we show how the nonseparable structure of polarization and spatial modes in vector beams is naturally described by a non-Abelian Chern-Simons gauge theory. In this framework, we link the Chern-Simons charge to spin-orbit coupling. This new insight on vector beams opens new possibilities for realizing and probing topological quantum field theories using classical optics, as well as laying the foundation for implementing topologically protected classical and quantum information protocols with structured light.

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• Angular momentum of light
• Structured light
• Topological effects in photonic systems
• Chern-Simons gauge theory
• Geometry